Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-03T19:30:02.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic slip wall model for large-eddy simulation

Published online by Cambridge University Press:  16 November 2018

Hyunji Jane Bae Open the ORCID record for Hyunji Jane Bae [Opens in a new window] ,
Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window] ,
Sanjeeb T. Bose  and
Parviz Moin
Hyunji Jane Bae*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA
Adrián Lozano-Durán
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Sanjeeb T. Bose
Affiliation:
Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA Cascade Technologies Inc., 2445 Faber Place, Suite 100, Palo Alto, CA 94303, USA
Parviz Moin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: hjbae@stanford.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Wall modelling in large-eddy simulation (LES) is necessary to overcome the prohibitive near-wall resolution requirements in high-Reynolds-number turbulent flows. Most existing wall models rely on assumptions about the state of the boundary layer and require a priori prescription of tunable coefficients. They also impose the predicted wall stress by replacing the no-slip boundary condition at the wall with a Neumann boundary condition in the wall-parallel directions while maintaining the no-transpiration condition in the wall-normal direction. In the present study, we first motivate and analyse the Robin (slip) boundary condition with transpiration (non-zero wall-normal velocity) in the context of wall-modelled LES. The effect of the slip boundary condition on the one-point statistics of the flow is investigated in LES of turbulent channel flow and a flat-plate turbulent boundary layer. It is shown that the slip condition provides a framework to compensate for the deficit or excess of mean momentum at the wall. Moreover, the resulting non-zero stress at the wall alleviates the well-known problem of the wall-stress under-estimation by current subgrid-scale (SGS) models (Jiménez & Moser, AIAA J., vol. 38 (4), 2000, pp. 605–612). Second, we discuss the requirements for the slip condition to be used in conjunction with wall models and derive the equation that connects the slip boundary condition with the stress at the wall. Finally, a dynamic procedure for the slip coefficients is formulated, providing a dynamic slip wall model free of a priori specified coefficients. The performance of the proposed dynamic wall model is tested in a series of LES of turbulent channel flow at varying Reynolds numbers, non-equilibrium three-dimensional transient channel flow and a zero-pressure-gradient flat-plate turbulent boundary layer. The results show that the dynamic wall model is able to accurately predict one-point turbulence statistics for various flow configurations, Reynolds numbers and grid resolutions.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 400 - 432
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, W. & Meneveau, C. 2011 Dynamic roughness model for large-eddy simulation of turbulent flow over multiscale, fractal-like rough surfaces. J. Fluid Mech. 679, 288–314.Google Scholar
Antonia, R. A., Fulachier, L., Krishnamoorthy, L. V., Benabid, T. & Anselmet, F. 1988 Influence of wall suction on the organized motion in a turbulent boundary layer. J. Fluid Mech. 190, 217–240.Google Scholar
Bae, H. J. & Lozano-Durán, A. 2017 Towards exact subgrid-scale models for explicitly filtered large-eddy simulation of wall-bounded flows. CTR Annu. Res. Briefs, pp. 207–214. Center for Turbulence Research.Google Scholar
Bae, H. J., Lozano-Durán, A., Bose, S. T. & Moin, P. 2018 Turbulence intensities in large-eddy simulation of wall-bounded flows. Phys. Rev. Fluids 3, 014610.Google Scholar
Bae, H. J., Lozano-Durán, A. & Moin, P. 2016 Investigation of the slip boundary condition in wall-modeled LES. CTR Annu. Res. Briefs, pp. 75–86. Center for Turbulence Research.Google Scholar
Balaras, E., Benocci, C. & Piomelli, U. 1996 Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34 (6), 1111–1119.Google Scholar
Bose, S. T.2012 Explicitly filtered large-eddy simulation: with application to grid adaptation and wall modeling. PhD thesis, Stanford University.Google Scholar
Bose, S. T. & Moin, P. 2014 A dynamic slip boundary condition for wall-modeled large-eddy simulation. Phys. Fluids 26 (1), 015104.Google Scholar
Bose, S. T. & Park, G. I. 2018 Wall-modeled LES for complex turbulent flows. Annu. Rev. Fluid Mech. 50 (1), 535–561.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. B. 2004 Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour. Res. 40 (2), 216–227.Google Scholar
Cabot, W. H. & Moin, P. 2000 Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow Turbul. Combust. 63, 269–291.Google Scholar
Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAA J. 17 (12), 1293–1313.Google Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Phys. Fluids 24 (1), 011702.Google Scholar
Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309.Google Scholar
Chung, Y. M. & Sung, H. J. 2001 Initial relaxation of spatially evolving turbulent channel flow with blowing and suction. AIAA J. 39 (11), 2091–2099.Google Scholar
Deardorff, J. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41 (1970), 453–480.Google Scholar
Del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329–358.Google Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J. 2017 Coherent structures in homogeneous shear turbulence compared with those in channels. J. Fluid Mech. 816, 167–208.Google Scholar
Flores, O. & Jiménez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357–376.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.Google Scholar
Ghosal, S. & Moin, P. 1995 The basic equations for the large eddy simulation of turbulent flows in complex geometry. J. Comput. Phys. 118 (1), 24–37.Google Scholar
Giometto, B. M. G., Lozano-Durán, A., Park, G. I. & Moin, P. 2017 Three-dimensional transient channel flow at moderate Reynolds numbers: analysis and wall modeling. CTR Annu. Res. Briefs, pp. 193–205. Center for Turbulence Research.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.Google Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.Google Scholar
Jiménez, J. & Moser, R. D. 2000 Large-eddy simulations: where are we and what can we expect? AIAA J. 38 (4), 605–612.Google Scholar
Kawai, S. & Larsson, J. 2013 Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers. Phys. Fluids 25 (1), 015105.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Larsson, J., Kawai, S., Bodart, J. & Bermejo-Moreno, I. 2016 Large eddy simulation with modeled wall-stress: recent progress and future directions. Mech. Engng Rev. 3 (1), 1–23.Google Scholar
Lee, J., Cho, M. & Choi, H. 2013 Large eddy simulations of turbulent channel and boundary layer flows at high Reynolds number with mean wall shear stress boundary condition. Phys. Fluids 25 (11), 110808.Google Scholar
Leonard, A. 1975 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237–248.Google Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.Google Scholar
Lozano-Durán, A. & Bae, H. J. 2016 Turbulent channel with slip boundaries as a benchmark for subgrid-scale models in LES. CTR Annu. Res. Briefs, pp. 97–103. Center for Turbulence Research.Google Scholar
Lozano-Durán, A., Bae, H. J., Bose, S. T. & Moin, P. 2017 Dynamic wall models for the slip boundary condition. CTR Annu. Res. Briefs, pp. 229–242. Center for Turbulence Research.Google Scholar
Lozano-Durán, A., Hack, M. J. P. & Moin, P. 2018 Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations. Phys. Rev. Fluids 3, 023901.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014a Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014b Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.Google Scholar
Luchini, P. 2017 Universality of the turbulent velocity profile. Phys. Rev. Lett. 118, 224501.Google Scholar
Lund, T. S. 2003 The use of explicit filters in large eddy simulation. Comput. Math. Appl. 46 (4), 603–616.Google Scholar
Lund, T. S. & Kaltenbach, H. J. 1995 Experiments with explicit filtering for les using a finite-difference method. CTR Annu. Res. Briefs, pp. 91–105. Center for Turbulence Research.Google Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140 (2), 233–258.Google Scholar
Marsden, A. L., Vasilyev, O. V. & Moin, P. 2002 Construction of commutative filters for LES on unstructured meshes. J. Comput. Phys. 175 (2), 584–603.Google Scholar
Millikan, C. M. 1938 A critical discussion of turbulent flows in channels and circular tubes. In Proceedings of the Fifth International Congress for Applied Mathematics, Harvard and MIT.Google Scholar
Mizuno, Y. & Jiménez, J. 2013 Wall turbulence without walls. J. Fluid Mech. 723, 429–455.Google Scholar
Moin, P., Shih, T. H., Driver, D. & Mansour, N. N. 1990 Direct numerical simulation of a three dimensional turbulent boundary layer. Phys. Fluids A 2 (10), 1846–1853.Google Scholar
Nikitin, N. 2007 Spatial periodicity of spatially evolving turbulent flow caused by inflow boundary condition. Phys. Fluids 19 (9), 091703.Google Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Fluid Flow Phenomena: A Numerical Toolkit 1. Springer.Google Scholar
Österlund, J. M.1999 Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, Mekanik.Google Scholar
Park, G. I. & Moin, P. 2014 An improved dynamic non-equilibrium wall-model for large eddy simulation. Phys. Fluids 26 (1), 015108.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397–411.Google Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.Google Scholar
Piomelli, U., Ferziger, J., Moin, P. & Kim, J. 1989 New approximate boundary conditions for large eddy simulations of wall-bounded flows. Phys. Fluids A 1 (6), 1061–1068.Google Scholar
Prandtl, L. 1925 Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z. Angew. Math. Mech. 5, 136–139.Google Scholar
Rozema, W., Bae, H. J., Moin, P. & Verstappen, R. 2015 Minimum-dissipation models for large-eddy simulation. Phys. Fluids 27 (8), 085107.Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.Google Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25 (10), 105102.Google Scholar
Silvis, M. H., Trias, F. X., Abkar, M, Bae, H. J., Lozano-Durán, A. & Verstappen, R. 2016 Exploring nonlinear subgrid-scale models and new characteristic length scales for large-eddy simulation. CTR Annu. Res. Briefs, pp. 265–274. Center for Turbulence Research.Google Scholar
Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228 (11), 4218–4231.Google Scholar
Simpson, R. L., Moffat, R. J. & Kays, W. M. 1969 The turbulent boundary layer on a porous plate: experimental skin friction with variable injection and suction. Intl J. Heat Mass Transfer 12 (7), 771–789.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91 (3), 99–164.Google Scholar
Spalart, P. R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41, 181–202.Google Scholar
Spalart, P. R., Jou, W. H., Strelets, M. & Allmaras, S. R. 1997 Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. Adv. DNS/LES 1, 4–8.Google Scholar
Stokes, G. G.1901 Mathematical and Physical Papers. Cambridge University Press.Google Scholar
Townsend, A. A. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Wang, M. & Moin, P. 2002 Dynamic wall modeling for large-eddy simulation of complex turbulent flows. Phys. Fluids 14 (7), 2043–2051.Google Scholar
White, F. M. & Corfield, I. 2006 Viscous Fluid Flow, vol. 3. McGraw-Hill.Google Scholar
Wray, A. A.1990 Minimal-storage time advancement schemes for spectral methods. Tech. Rep. NASA Ames Research Center.Google Scholar
Yamamoto, Y. & Tsuji, Y. 2018 Numerical evidence of logarithmic regions in channel flow at Re 𝜏 = 8000. Phys. Rev. Fluids 3, 012602.Google Scholar
Yang, X. I. A., Park, G. I. & Moin, P. 2017 Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations. Phys. Rev. Fluids 2, 104601.Google Scholar
Yang, X. I. A., Sadique, J., Mittal, R. & Meneveau, C. 2015 Integral wall model for large eddy simulations of wall-bounded turbulent flows. Phys. Fluids 27 (2), 025112.Google Scholar
Yoshioka, S. & Alfredsson, P. H. 2006 Control of Turbulent Boundary Layers by Uniform Wall Suction and Blowing. pp. 437–442. Springer.Google Scholar